I just added another support email address and I want to be the only agent to receive tickets coming to that particular address - Is this possible?

You can do this by creating a workflow Automator from Admin-->Workflow Automator-->New ticket Automator. Set the event as “Ticket is created”. Drag and drop a condition block into the workflow and provide the condition “To Email is” and provide the respective support email address. Now add an action block and choose the action as “Assign to Agent” and choose your name on the same.